KCLNet: Electrically Equivalence-Oriented Graph Representation Learning for Analog Circuits

2026-03-25

AI Summary

This work addresses the challenge of learning effective representations for analog circuits that preserve electrical equivalence, a task complicated by their continuous electrical characteristics. To this end, the paper proposes KCLNet, an asynchronous graph neural network grounded in Kirchhoff’s Current Law (KCL). KCLNet enforces explicit conservation of current at each node in the embedding space through an electrically inspired message-passing mechanism, thereby guiding representation learning toward electrical equivalence. As the first approach to integrate KCL into graph neural networks, KCLNet demonstrates significantly improved generalization performance across multiple tasks, including circuit classification, subcircuit detection, and edit distance prediction.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Computer Vision: Representation Learning for Vision
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Digital circuits representation learning has made remarkable progress in the electronic design automation domain, effectively supporting critical tasks such as testability analysis and logic reasoning. However, representation learning for analog circuits remains challenging due to their continuous electrical characteristics compared to the discrete states of digital circuits. This paper presents a direct current (DC) electrically equivalent-oriented analog representation learning framework, named \textbf{KCLNet}. It comprises an asynchronous graph neural network structure with electrically-simulated message passing and a representation learning method inspired by Kirchhoff's Current Law (KCL). This method maintains the orderliness of the circuit embedding space by enforcing the equality of the sum of outgoing and incoming current embeddings at each depth, which significantly enhances the generalization ability of circuit embeddings. KCLNet offers a novel and effective solution for analog circuit representation learning with electrical constraints preserved. Experimental results demonstrate that our method achieves significant performance in a variety of downstream tasks, e.g., analog circuit classification, subcircuit detection, and circuit edit distance prediction.

Problem

• analog circuits
• representation learning
• electrical characteristics
• graph representation

Innovation

• analog circuit representation learning
• Kirchhoff's Current Law (KCL)
• electrically equivalent embedding
• graph neural network
• electrical constraint